Fractals are mathematical images that are build up out of repeated elements. These elements are also changed a bit per repetition (shape, orientation, color, etc.) One of the most simple fractals is shown in figure 1. Here one of the sides of the triangle forms a side of the next square. One side of this square forms another triangle and then this proces is repeated again. There is symetrie in this figure because the short sides of the triangles have the same lenght.
Figure 1) Simple fractal.
Fractals can however become much more complex when there are more variables that change and especially when they influence eachother. Even though it looks like pure mathematics, these fractals can be found in nature as well, especially in growth patterns of dendritic structures.
To be continued...
 Fractal made with MS Paint by me.